There were moments when it looked like the glorious run of the New Big Three might be over.

Not yet. There’s at least one more round of playoffs for the Old Bones of Causeway Street. In a series that could have been sponsored by John Deere or Black & Decker, the Celtics defeated the Philadelphia 76ers, 85-75, in Game 7 of the Eastern Conference semifinals at the Garden on Saturday night. Boston’s Wheez Kids live to play another day. Time to bring on LeBron James and the Miami Heat, starting Monday night at AmericanAirlines Arena.

The Celtics went into Saturday night’s game with a 20-6 record in Game 7s, 17-4 on the parquet floor. Honoring Bill Russell, John Havlicek, Larry Bird, and the other gods in the rafters, the Green Team held off the brick-laying, eighth-seeded upstarts from Broad Street, but it was not easy. Nothing comes easily for the Celtics this year.

The Celtics won because Rajon Rondo (18 points, 10 rebounds, 10 assists) took over the game after captain Paul Pierce fouled out with 4:16 remaining. Rondo scored 9 points in less than two minutes to turn a 3-point lead into a 10-point lead with 1:45 remaining.

There are times when it appears that Messrs. Pierce, Allen, and Garnett might calcify in mid-shot. They are held together by duct tape as they lurch toward June but still are in contention for championship banner No. 18. They will be major underdogs against the Heat.

The Celtic-Sixers series goes down as one of the more inelegant jousts in NBA history. Purists might argue that the fortnight of brick-ball set the sport back 20 years. With San Antonio and Oklahoma City dueling for the Western crown, NBA commissioner David Stern (who was seated at courtside) had to be rooting for the Celtics to bring their star power to the conference finals. The 76ers are one of the more anonymous playoff entries of recent times and almost certainly would have been cannon fodder for the Heat.

The Celtics match up well with Miami but are staggering into late May without Avery Bradley (shoulder surgery) and with Pierce, Ray Allen and Kevin Garnett markedly diminished by age and injury.

The Celtics didn’t help their cause for the next round by letting the dogged Sixers extend the series to seven games. Boston lost Game 2 at the Garden by 1 point, then blew an 18-point lead in Philly in Game 4. The Celtics were unable to close it out Wednesday night in Philadelphia, and there was some fear that Saturday night would be the famous final scene for Pierce, Allen, and Garnett.

Miming the Red Auerbach Celtics of the 1960s, all five Boston starters hit for double figures in Saturday’s finale, but it was Rondo who took charge when Philly closed to within 3 with 4 1/2 minutes remaining.

With Pierce going to the bench with his sixth foul, Rondo took over the game.

No. With Allen struggling badly (3 for 11) and Pierce on the pine, Garnett worked with Rondo to keep the old guys alive.

“We were kind of down to Rondo and Kevin down the stretch,’’ acknowledged Celtics coach Doc Rivers.

“The Sixers are a pain,’’ he added. “ . . . They are a tough basketball team.’’

Philly shot only 28 percent in the first half, and 35 percent for the game, but still, the Sixers posed a threat. The visitors have won only one playoff series since 2003, but they never quit in seven games against the Hall of Famers from Boston.

The Celtics led for almost every second of Game 7, but the margin was down to 3 when Pierce went to the pine with his sixth foul for charging into Thaddeus Young.

Rondo Time. Boston’s triple-threat guard scored on a baseline drive, then hit a 24-foot jumper, a 27-foot trey, and a pair of free throws to put everyone’s mind at ease.

“I felt I had a pretty good rhythm,’’ said Rondo. “I wanted to stay confident and hit the shots. My teammates needed me to step up.’’

“We had a chance to win and then Rondo made some great plays,’’ said 76ers coach Doug Collins.

Saturday night’s game was played on the 25th anniversary of Bird’s game-winning steal against the Pistons in the 1987 conference finals. It’s always about history with the Celtics.

Boston’s next home game will be Friday night against James, Dwyane Wade, and the powerhouse Heat. The Celtics matched up well against Miami this season, but were thrashed by the Heat in five games of the conference semifinals last spring.

The 2012 Celtics don’t seem to have much left, but they can hold their heads high. They have exceeded all expectations and pushed themselves to the limit. And now it’s time to take their talents to South Beach.

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